鄒振城 劉厶元

基于非負(fù)矩陣分解的遞歸稀疏表示的心肺音分離方法

鄒振城 劉厶元

（廣東工業(yè)大學(xué)）

針對(duì)心肺音的時(shí)序結(jié)構(gòu)特性，提出一種基于非負(fù)矩陣分解的遞歸稀疏表示的心肺音分離方法。通過非負(fù)矩陣分解構(gòu)建能有效描述心肺音的遞歸特征心肺音字典；基于該字典，獲得心音和肺音的稀疏表示，實(shí)現(xiàn)心肺音分離。實(shí)驗(yàn)結(jié)果表明：本文設(shè)計(jì)的心肺音分離方法取得的效果優(yōu)于基于非負(fù)矩陣分解的稀疏表示的心肺音分離方法、監(jiān)督非負(fù)矩陣分解方法的心肺音分離和帶通濾波。

心肺音分離；非負(fù)矩陣分解；遞歸；稀疏表示

0　引言

據(jù)《World Health Statistics 2018: Monitoring health for the SDGs》報(bào)告[1]，心血管疾病和呼吸道疾病的發(fā)病率呈逐年上升趨勢(shì)。聽診是臨床常用的心血管和呼吸道疾病的診斷方法，傳統(tǒng)的心臟聽診依賴于醫(yī)生的臨床經(jīng)驗(yàn)[2-3]。然而，通過聽診器采集到的心音和肺音?；殳B在一起，影響聽診的有效性。因此，研究心肺音分離方法對(duì)提高聽診質(zhì)量，協(xié)助醫(yī)生進(jìn)行輔助診斷具有重要的現(xiàn)實(shí)意義。臨床采集的混合信號(hào)中，心音和肺音在60 Hz~320 Hz頻帶存在相互干擾。傳統(tǒng)的帶通濾波[4]僅適用于分離頻帶相互分離的源成分，無法有效地將心音和肺音完全區(qū)分開；自適應(yīng)濾波方法[5]和小波變換方法[6]性能依賴精確模板和參數(shù)選擇，難以實(shí)際推廣。

非負(fù)矩陣分解（non-negative matrix factorization，NMF）是一種常用盲分離方法[7]，通過抽取隨時(shí)間變化的心肺音幅模，能捕捉變換域重復(fù)出現(xiàn)的模式，適于心肺音分離。然而，基于監(jiān)督NMF的心肺音分離方法[8]忽略了肺音頻域模式復(fù)雜多樣的特點(diǎn)，分離效果欠佳?；谧值鋵W(xué)習(xí)的稀疏表示的單通道盲分離方法克服了以上的不足，并已廣泛用于信號(hào)處理，如無線通訊[9-10]和生物醫(yī)學(xué)[11]等領(lǐng)域。但是，以上方法都忽略了心肺音信號(hào)時(shí)序上的遞歸特性。

本文在基于NMF的稀疏表示的心肺音方法上進(jìn)行改進(jìn)，提出基于NMF的遞歸稀疏表示的心肺音分離方法，實(shí)現(xiàn)心肺音分離，從而提高心肺音分離的信噪比。

1　心肺音混合模型

臨床采集到心肺音混合信號(hào)可用式(1)線性混合模型表示[8]：

通過小波變換方法[12]濾除白噪聲后，可認(rèn)為心肺音混合信號(hào)只含有心音和肺音，其數(shù)學(xué)模型為

2　非負(fù)矩陣分解

利用梯度下降法可得到：

3　基于非負(fù)矩陣分解的遞歸稀疏表示

3.1　遞歸字典構(gòu)建

基于非負(fù)矩陣分解的遞歸稀疏表示的心肺音分離方法的構(gòu)造字典示意圖如圖1所示。

圖1　基于非負(fù)矩陣分解的遞歸稀疏表示的心肺音分離方法的構(gòu)造字典示意圖

3.2　稀疏表示

可轉(zhuǎn)化為二次規(guī)劃問題求解：

3.3　重構(gòu)心肺音

時(shí)頻掩碼是基于心臟和呼吸聲信號(hào)稀疏的假 設(shè)[13]，在一個(gè)小時(shí)頻區(qū)域只有一個(gè)源信號(hào)占主導(dǎo)地位。

應(yīng)用時(shí)頻掩模和混合信號(hào)的時(shí)頻譜以恢復(fù)源成分：

再利用逆短時(shí)傅里葉變換(inverse short-time Fourier transform, ISTFT）將恢復(fù)的源成分轉(zhuǎn)換成時(shí)域信號(hào)。

4　實(shí)驗(yàn)

4.1　實(shí)驗(yàn)設(shè)置

為驗(yàn)證本文提出的基于NMF的遞歸稀疏表示的心肺音分離方法的有效性，將該方法在一個(gè)自構(gòu)的心肺音數(shù)據(jù)集進(jìn)行測試。測試數(shù)據(jù)集來源于公開的數(shù)據(jù)集[14-21]，包含112條干凈的心音信號(hào)，其中正常21條，異常91條；36條干凈的肺音信號(hào)，其中正常10條，異常26條。由于在不同公開數(shù)據(jù)集中篩選出的信號(hào)具有不同的信號(hào)長度和采樣頻率，本文將信號(hào)截取為10 s，降采樣至2 kHz采樣頻率。本文仿真實(shí)驗(yàn)以干凈的心音和肺音信號(hào)按1:1能量比線性混合成的心肺音混合信號(hào)為輸入信號(hào)，通過計(jì)算分離得到的心音和肺音信號(hào)來評(píng)估心肺音分離性能。越高，表示心肺音分離性能越好。

實(shí)驗(yàn)中，STFT采用窗長為128個(gè)采樣點(diǎn)的漢寧窗，窗口的移動(dòng)步長為32個(gè)采樣點(diǎn)，傅里葉變換長度為128。

圖2　心音、肺音和心肺音混合信號(hào)時(shí)頻譜

圖3　干凈心音、干凈肺音、混合心肺音和分離后的心音、肺音時(shí)域圖

4.2　實(shí)驗(yàn)結(jié)果和分析

表1比較了帶通濾波、監(jiān)督NMF、基于NMF的稀疏表示和基于NMF的遞歸稀疏表示的心肺音分離性能。與帶通濾波、監(jiān)督NMF和基于NMF的稀疏表示相比，基于NMF的遞歸稀疏表示方法分離出來的心音信噪比提高了4.09 dB，0.58 dB和0.2 dB，肺音信噪比提高了4.01 dB，0.52 dB 和0.15 dB。表明基于NMF的遞歸稀疏表示的心肺音分離方法具有更優(yōu)的心肺音分離性能。

表1　實(shí)驗(yàn)結(jié)果對(duì)比

5　結(jié)語

針對(duì)心肺音的時(shí)序結(jié)構(gòu)特性，本文提出一種基于NMF的遞歸稀疏表示的心肺音分離方法。在公開心肺音數(shù)據(jù)集上的仿真結(jié)果表明：相較于帶通濾波、監(jiān)督NMF和基于NMF的稀疏表示，基于NMF的遞歸稀疏表示取得更優(yōu)的分離效果。

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Cardiopulmonary Sound Separation Method Based on Recursive Sparse Representation of Non-Negative Matrix Factorization

Zou Zhencheng Liu Siyuan

(Guangdong University of Technology)

In order to address the time-series structure characteristics of cardiopulmonary sound, a method of heart-lung sound separation based on recursive sparse representation of non-negative matrix factorization is proposed. The recursive feature cardiopulmonary dictionary which can effectively describe cardiopulmonary sound is constructed by non-negative matrix factorization. Based on this dictionary, we get a sparse representation of heart sounds and lung sounds to achieve separation of heart and lung sounds. The experimental results show that the cardiopulmonary separation method is designed in this paper achieves a cardiopulmonary separation method superior to the sparse representation based on non-negative matrix factorization, and supervises the cardiopulmonary separation and band pass filtering effects of the non-negative matrix factorization method.

Cardiopulmonary Separation; Non-Negative Matrix Factorization; Recursion; Sparse Representation

鄒振城，男，1994年生，碩士研究生，主要研究方向：模式識(shí)別，機(jī)器學(xué)習(xí)，生物信號(hào)處理。E-mail: walnmm@126.com